https://file.aiquickdraw.com/mathbot/file/1730676869208zuzeng46.jpg

To determine where the function \( f(x) \) is decreasing, we need to analyze the intervals where the graph has a downward slope, meaning \( f(x) \) decreases as \( x \) increases. This is typically seen where the graph moves down from left to right.

### Step-by-Step Analysis

1. **Identify Decreasing Intervals on the Graph**:
   - From the image, observe that the graph of \( f(x) \) decreases on two specific intervals:
     - Starting from the left, it decreases from approximately \( x = -\infty \) to around \( x = -2 \).
     - The graph also decreases from approximately \( x = 1 \) to \( x = 4 \).

2. **Conclusion**:
   - Therefore, the intervals where \( f(x) \) is decreasing are:
     \[
     (-\infty, -2) \quad \text{and} \quad (1, 4).
     \]

Would you like more details on how to find these intervals or have any questions? 

---

### Related Questions for Practice
1. How do you determine where a function is increasing on an interval?
2. What is the significance of critical points in finding increasing or decreasing intervals?
3. How does the derivative of a function help identify increasing and decreasing intervals?
4. What would change in the intervals if the graph was shifted up or down?
5. How can you tell if a function is constant over an interval?

### Tip
To verify decreasing intervals analytically, take the derivative of \( f(x) \) and identify where \( f'(x) < 0 \).

Determine all intervals on which the graph of f is decreasing.

Learn how to determine all intervals on which a function graph is decreasing. This example explains graph analysis techniques, including how to identify decreasing intervals by observing slope changes. Suitable for students in Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation